In-plane free vibration analysis for rectangular plates with elastically restrained edges by Differential Quadrature Method
Pu Yu ，Teng Zhao-chun ，ZHAO Hai-ying
1. School of Civil Engineering，Lanzhou Institute of Technology，Lanzhou 730050，China；
2. Department of Engineering Mechanics, College of Science, Lanzhou University of Technology, Lanzhou 730050, China
Abstract：Based on the two-dimension theory of linear elasticity, applied the Hamilton's principle, the in-plane free vibration of governing partial differential equations for rectangular plates with elastically restrained edges are derived. Using differential quadrature method (DQM), the dimensionless frequencies of in-plane free vibration of rectangular plates with elastically restrained edges are investigated. All the classical boundaries for in-plane displacements can be simulated by setting the stiffnesses of the restraining springs to either zero or infinite. The application of DQM in this paper have illustrated the analytical method was validated and accurate by comparison of previously reported results with those available in the literature for rectangular plates. Finally, The influence of the boundary conditions, geometrical parameter, and stiffness coefficients on the dimensionless frequencies of the rectangular plates are investigated.
[1] Lyon R H. In-plane contribution to structural noise transmission[J]. Noise Control Engineering Journal, 1986, 26(1): 22-27.
[2] Langley R S, Bercin A N. Wave intensity analysis of high frequency vibration[J]. Philosophical Transactions of the Royal Society of London A, 1994, 346, 489-499.
[3] Bercin A N. An assessment of the effect of in-plane vibration on the energy flow between coupled plates[J]. Journal of Sound and Vibration, 1996, 191(5): 661-680.
[4] Bardell N S, Langley R S, Dunsdon J M. On the free in-plane vibration of isotropic rectangular plates[J]. Journal of Sound and Vibration, 1996, 191(3): 459-467.
[5] Farag N H, Pan J. Free and force in-plane vibration of rectangular plates[J]. Acoustical Society of America, 1998, 103(1): 408-413.
[6] Wang G, Wereley N M. Free in-plane vibration of rectangular plates[J]. AIAA, 2002, 40(5): 953-959.
[7] Gorman D G. Free in-plane vibration analysis of rectangular plates by the method superposition[J]. Journal of Sound and Vibration, 2004, 272(3): 831-851.
[8] Gorman D G. Exact solutions for the free in-plane vibration of rectangular plates with two opposite edges simply supported[J]. Journal of Sound and Vibration, 2006, 294(1): 131-161.
[9] Du Jingtao, Li Wen L, Jin Guoyong, et al. An analytical method for the in-plane vibration analysis of rectangular plates with elastically restrained edges[J]. Journal of Sound and Vibration, 2007, 306(3-5): 908-927.
[10] Xing Y F, Liu B. Exact solutions for the free in-plane vibrations of rectangular plates[J]. International Journal of Mechanical Sciences, 2009, 51(3): 246-255.
[11] Liu Bo, Xing Yufeng. Exact solutions for free in-plane vibration of rectangular plates[J]. Acta Mechanica Solida Sinica, 2011, 24(6): 556-567.
[12] Bert C W, Malik M. Differential quadrature method in computational mechanics[J]. Applied Mechanics Reviews, 1996, 49(1): 1-27.
[13] 蒲育, 滕兆春, 房晓林. 圆环板面内自由振动的DQM求解[J]. 振动与冲击, 2013, 32(24): 152-156. Pu Yu, Teng Zhao-chun, Fang Xiao-lin. In-plane free vibration of circular annular plates with differential quadrature method[J]. Journal of Vibration and Shock, 2013, 32(24): 152-156.
[14] 滕兆春，蒲育. 温度影响下FGM圆环板的面内自由振动分析[J]. 振动与冲击，2015, 34(9): 223-230. Teng Zhao-chun, Pu Yu. In-plane free vibration of FGM annular plates considering temperature effect[J]. Journal of Vibration and Shock, 2015, 34(9): 223-230.
